Darboux transformations for 5-point and 7-point self-adjoint schemes and an integrable discretization of the 2D Schrödinger operator
| Autor: | Maciej Nieszporski, Paolo Maria Santini, Adam Doliwa |
|---|---|
| Rok vydání: | 2004 |
| Předmět: |
Physics
Pure mathematics Nonlinear Sciences - Exactly Solvable and Integrable Systems Discretization Integrable system Darboux frame FOS: Physical sciences General Physics and Astronomy Darboux integral Schrödinger equation symbols.namesake Nonlinear Sciences::Exactly Solvable and Integrable Systems Operator (computer programming) Elliptic partial differential equation symbols Exactly Solvable and Integrable Systems (nlin.SI) Self-adjoint operator |
| Zdroj: | Physics Letters A. 323:241-250 |
| ISSN: | 0375-9601 |
| DOI: | 10.1016/j.physleta.2004.02.003 |
| Popis: | With this paper we begin an investigation of difference schemes that possess Darboux transformations and can be regarded as natural discretizations of elliptic partial differential equations. We construct, in particular, the Darboux transformations for the general self adjoint schemes with five and seven neighbouring points. We also introduce a distinguished discretization of the two-dimensional stationary Schrodinger equation, described by a 5-point difference scheme involving two potentials, which admits a Darboux transformation. 15 pages, 1 figure |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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